Connected regular graphs with girth at least 4

The following table contains numbers of connected regular graphs having girth at least four and with the given degree and number of vertices. The (k,4) cage is K_{k,k}.

Not necessarily connected 2-regular with girth exactly 4 are counted by A026797.

Not necessarily connected 2-regular with girth at least 4 are counted by A008484.

Girth at least: 3 4 5 6 7 8

  A014371 A033886 A058275 A058276
Vertices Degree 3 Degree 4 Degree 5 Degree 6 Degree 7 Degree 8 Degree 9 Degree 10
6 1
7 0
8 2 1
9 0 0
10 6 2 1
11 0 2 0
12 22 12 1 1
13 0 31 0 0
14 110 220 7 1 1
15 0 1606 0 1 0
16 792 16828 388 9 1 1
17 0 193900 0 6 0 0
18 7805 2452818 406824 267 8 1 1
19 0 32670330 0 3727 0 0 0
20 97546 456028474 1125022325 483012 741 13 1 1
21 0 6636066099 0 69823723 0 1 0 0
22 1435720 100135577747 3813549359274       14 1
23 0
24 23780814
25 0
26 432757568
27 0
28 8542471494
29 0
30 181492137812